The energy stored in a parallel-plate capacitor can be calculated using the formula Uc = (Q^2)/(2C). In this case, the energy stored after the separation is decreased can be found by calculating the new capacitance and using the formula Uc = (Q^2)/(2C). The energy stored after the change is 2.02 J.
The energy stored in a parallel-plate vacuum capacitor is given by the formula Uc = (Q^2)/(2C), where Uc is the energy, Q is the charge stored in the capacitor, and C is the capacitance. The energy is directly proportional to the square of the charge and inversely proportional to the capacitance. In this case, the energy before the separation is changed is given as 8.80 J. When the separation is decreased from 2.80 mm to 1.65 mm, the capacitance decreases and the charge remains constant. Therefore, the energy stored after the separation is changed can be found using the formula Uc = (Q^2)/(2C).
Given that the separation before the change is d1 = 2.80 mm and the separation after the change is d2 = 1.65 mm, we can find the capacitances C1 and C2 using the formula C = (ε0 * A) / d, where ε0 is the vacuum permittivity, A is the area of the plates, and d is the separation. Substitute the values to find the capacitances C1 and C2. Then, use the formula Uc = (Q^2)/(2C) to find the energies Uc1 and Uc2 corresponding to the capacitances C1 and C2.
Therefore, the energy stored after the separation is changed is Uc2 = 2.02 J.